How do I know it's time to get a new laptop?

Let's not jump to the upgrade solution too quickly. First, take a look at the performance benchmarks of the hardware you have against those of the hardware recommended for the tasks you perform. That will give you direct information about whether or not your laptop is really up to the task. If\ your hardware is up to even medium performance of those activities, you probably don't want to /need to upgrade.

Steps to try to resolve the issue:

First, install your freeware of choice to monitor the CPU and GPU temps of the machine.

Second, take a can of canned air and blow it through the intake and exhaust fans until no more dust comes out. You will probably want to do this outside, particularly if you haven't done it before.

Third, the screws aren't a problem because of crud or age, it is because a liquid called (I believe) Lock-Tite was used on the screws. If you get one out it should have a little blue stuff on the screw. This is to keep screws from coming out on their own and to deter the casual effort at getting inside. You will want a size 0 Philips screwdriver, perhaps even smaller to take these out. The precision/jewelers screw drivers would work well except that sometimes they are hard to turn because they don't have a larger diameter handle. In those cases, if I don't have a small bit with a large enough grip I push down on the screwdriver with one hand and turn the driver with a pair of pliers until the screw is loose enough to use the screw driver directly. If you search for your laptop model and "disassemble" or some variant thereof, you should find an easy to follow video or write-up. This will allow you to get to the heat sink and remove things you couldn't blow out with air, such as animal fur or hair.

Assuming that it is clean and continues to misbehave, one last thing I can think of doing is to back up all your personal data off the machine and then perform a factory restore, install your AV program, run Windows update until you get no more updates, install your third party apps and restore your files.

Don't take it to geek squad. You will pay a pretty big part of what you would pay for a new laptop. This could be any number of issues, but you'd really have to open the laptop to find out. Most people buy new laptops every 4 years or so, sometimes more frequently, so it may be appropriate to make the purchase.

In my opinion its a smarter idea to get a new laptop. One reason being between '09/'10 technology has changed SO much and its probably time for a step into the new technology. Another reason being if one thing is failing, and others are starting too, then more and more is going to fail, and you'll spend more time at Geek Squad then using it at that point. So in my opinion its smarter to get a new laptop.

Yes, I think it's time to change; I also have a 2009 laptop and I recently bought a a new one because the other one was a hot mess.

Have you removed the cover from the heatsink/fan assembly and cleaned it all out and replaced the heatsink paste with arctic silver?